{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:TRVMC5K3YOYPEOAMBH5B5LEZC4","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"edc0762367b5ce3eba04ec7a93343325259880c81b698791fe06139ca9d89269","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-08-11T15:41:17Z","title_canon_sha256":"993efde7e90bd0f8929bd1d8762bfffabfbacc1cee815f1d1f54a8ce7d1b64be"},"schema_version":"1.0","source":{"id":"1408.2445","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.2445","created_at":"2026-05-18T01:28:14Z"},{"alias_kind":"arxiv_version","alias_value":"1408.2445v3","created_at":"2026-05-18T01:28:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.2445","created_at":"2026-05-18T01:28:14Z"},{"alias_kind":"pith_short_12","alias_value":"TRVMC5K3YOYP","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"TRVMC5K3YOYPEOAM","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"TRVMC5K3","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:89f4e19a16ddbec815eab3721dec1975d737832ffc39cc404453c4ca21987a2b","target":"graph","created_at":"2026-05-18T01:28:14Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We construct a class of rank-one infinite measure-preserving transformations such that for each transformation $T$ in the class, the cartesian product $T\\times T$ of the transformation with itself is ergodic, but the product $T\\times T^{-1}$ of the transformation with its inverse is not ergodic. We also prove that the product of any rank-one transformation with its inverse is conservative, while there are infinite measure-preserving conservative ergodic Markov shifts whose product with their inverse is not conservative.","authors_text":"Cesar E. Silva, Indraneel Kasmalkar, Isaac Loh, Julien Clancy, Rina Friedberg, Sahana Vasudevan, Tudor P\\u{a}durariu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-08-11T15:41:17Z","title":"Ergodicity and Conservativity of products of infinite transformations and their inverses"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2445","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:e52dbb759ba54ea2f6699b31fcc5e7ca46f5c244cb4d5015675bfa6f824b4259","target":"record","created_at":"2026-05-18T01:28:14Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"edc0762367b5ce3eba04ec7a93343325259880c81b698791fe06139ca9d89269","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-08-11T15:41:17Z","title_canon_sha256":"993efde7e90bd0f8929bd1d8762bfffabfbacc1cee815f1d1f54a8ce7d1b64be"},"schema_version":"1.0","source":{"id":"1408.2445","kind":"arxiv","version":3}},"canonical_sha256":"9c6ac1755bc3b0f2380c09fa1eac991739b7079736e2c959d9f745a9d306bc65","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c6ac1755bc3b0f2380c09fa1eac991739b7079736e2c959d9f745a9d306bc65","first_computed_at":"2026-05-18T01:28:14.843667Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:14.843667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"loBJqwsn+5EsbpVBY4nCNZBtVbqaul1QrkZdZmepn4auPe0asE3ACecmUnPqaA0XTxwefwpy4MuwoAJ7+mB4Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:14.844332Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.2445","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e52dbb759ba54ea2f6699b31fcc5e7ca46f5c244cb4d5015675bfa6f824b4259","sha256:89f4e19a16ddbec815eab3721dec1975d737832ffc39cc404453c4ca21987a2b"],"state_sha256":"7f235c81809590248416a4008a2942064905c3f839e75195fbcc4f5acb3ccaa5"}